Refer to Exercise 15.28. a. Plot the data in a profile plot with factors job type a...

Refer to Exercise 15.28.

a. Plot the data in a profile plot with factors job type and region. Does there appear to be an interaction between the two factors? If there was an interaction, would you be able to test for it using the given data? If not, why not?

b. Did the geographical region variable increase the efficiency of the design over conducting the study as a completely randomized design where the city manager would have just randomly selected eight cities regardless of their location?

c. Identify additional sources of variability that may need to be included in future studies.

REFERENCE:

15.28 : The city manager of a large midwestern city was negotiating with the three unions that represented the policemen, firemen, and building inspectors over the salaries for these groups of employees. The three unions claimed that the starting salaries were substantially different between the three groups, whereas in most cities there was not a significant difference in starting salaries between the three groups. To obtain information on starting salaries across the nation, the city manager decided to randomly select one city in each of eight geographical regions. The starting yearly salaries (in thousands of dollars) were obtained for each of the three groups in each of the eight regions. The data appear here.

a. Write a model for this study, identifying all the terms in the model.

b. Using the analysis of variance from the Minitab computer output shown here, do the data suggest a difference in mean starting salary for the three groups of employees? Use α = .05.

c. Give the level of significance for your test.

d. Which pairs of jobs types have significantly different starting salaries?